Inspiration from physics for thinking about economics, finance and social systems

Monday, March 18, 2013

New territory for game theory...

This new paper in PLoS looks fascinating. I haven't had time yet to study it in detail, but it appears to make an important demonstration of how, when thinking about human behavior in strategic games, fixed point or mixed strategy Nash equilibria can be far too restrictive and misleading, ruling out much more complex dynamics, which in reality can occur even for rational people playing simple games:

Abstract

Recent
theories from complexity science argue that complex dynamics are
ubiquitous in social and economic systems. These claims emerge from the
analysis of individually simple agents whose collective behavior is
surprisingly complicated. However, economists have argued that iterated
reasoning–what you think I think you think–will suppress complex
dynamics by stabilizing or accelerating convergence to Nash equilibrium.
We report stable and efficient periodic behavior in human groups
playing the Mod Game, a multi-player game similar to
Rock-Paper-Scissors. The game rewards subjects for thinking exactly one
step ahead of others in their group. Groups that play this game exhibit
cycles that are inconsistent with any fixed-point solution concept.
These cycles are driven by a “hopping” behavior that is consistent with
other accounts of iterated reasoning: agents are constrained to about
two steps of iterated reasoning and learn an additional one-half step
with each session. If higher-order reasoning can be complicit in complex
emergent dynamics, then cyclic and chaotic patterns may be endogenous
features of real-world social and economic systems.

...and from the conclusions, ...

Cycles in the belief space of learning agents have been predicted for
many years, particularly in games with intransitive dominance relations,
like Matching Pennies and Rock-Paper-Scissors, but experimentalists
have only recently started looking to these dynamics for experimental
predictions. This work should function to caution experimentalists of
the dangers of treating dynamics as ephemeral deviations from a static
solution concept. Periodic behavior in the Mod Game, which is stable and
efficient, challenges the preconception that coordination mechanisms
must converge on equilibria or other fixed-point solution concepts to be
promising for social applications. This behavior also reveals that
iterated reasoning and stable high-dimensional dynamics can coexist,
challenging recent models whose implementation of sophisticated
reasoning implies convergence to a fixed point [13].
Applied to real complex social systems, this work gives credence to
recent predictions of chaos in financial market game dynamics [8].
Applied to game learning, our support for cyclic regimes vindicates the
general presence of complex attractors, and should help motivate their
adoption into the game theorist’s canon of solution concepts

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Physicist and science writer. I was formerly an editor with the international science journal Nature and also the magazine New Scientist. I am the author of three earlier books, and have written extensively for publications including Nature, Science, the New York Times, Wired and the Harvard Business Review. I currently write monthly columns for Nature Physics and for Bloomberg Views.